The very designs of the Gundams found in this show, which are seen as so utterly ridiculous and improbable for the various series in the granddaddy of the Real Robot Genre. Let's see here:
To start, the Nobel Gundam, which got stripped straight from Sailor Moon and made into a Gundam.
The Tequila Gundam. They had to put a Mexican hat on it, do they?
One of the OSTs comes with an audio play that sees the characters attending the premiere of a movie based off of their adventures. The entire story is one long CMOF, with notable moments including the movie swapping Rain and Sai Saici's roles (making Rain part of the Five-Man Band and Sai the Distressed Damsel, to the real Sai's annoyance) and a scene where the heroes stand at the base of Tokyo Tower and shout up at Master Asia, with the conversation rapidly becoming distorted and confused due to the distance.
While breaking out of the Russian prison, Domon runs into an enormous, muscular man blocking his path. Domon immediately starts punching him in the stomach, but the man's stern facial expression doesn't change an iota. Then he knocks out Domon by smacking him on the head. And thus Domon met Argo Gulskii.
While training, Sai Saici drops in to cause some mischief, even lifting up Rain's skirt and showing her white panties. After he runs off into the distance, Rain asks Domon if he saw. His answer? He turns beet red and falls underwater.
Sai Saici drops in on Domon at the place he's staying during the finals. He arrives speeding on a bike with a few bags of groceries and a wok, only to trip and lose control as everything goes flying, but manages to regain his balance, catch the bike and the bags perfectly without spilling a thing. Then the wok hits him on his head and he falls over and spills everything.
The announcer contrasts Chibodee's Hot-Blooded and hammy, American entrance to the Finals match with Domon's steady walk, reflecting the Japanese traditions of "calm and simplicity." Yes, DomonKasshu is being described as embodying the virtue of calm without any trace of irony.
Allenby's complete lack of acknowledgement for rules and national protocol. She sees zero problems in giving proprietary Swedish upgrades to God Gundam, and when Chairman Karato protests her actually getting onto Neo-Japan's control platform to advise Domon she just says "shut up, old-timer!"
After everyone is flipping out over the impossibility of the "God Shadow" technique, where Domon somehow duplicates his Gundam enough times to catch every strike from Chibodee's Bursting Machine-Gun Punch, Allenby's only comment is a thumbs-up and a "Yeah! The training helped!"
When Sai Saici is being threatened by three guys in construction robots, Domon steps in using Burning Gundam (which in the dub he calls "Shining Gundam"). The guys run around Domon at high speed (they call it a jetstream attack, a Shout-Out to the Black Tri-Stars of the original Gundam) kicking up so strong wind, only for Domon to stick his foot out to trip one, causing the others to slam into their buddy and fall over a rail into the water. Just for kicks, Burning Gundam's hands and doing a "job well done" gesture.
The original manga adaptation gave us a backup feature, Go For It, Domon! - a Yonkoma featuring the G Gundam characters taken out of canonical events and played off of each other for laughs. The entire strip runs on Rule of Funny, and one Running Gag has Fuunsaiki (Master Asia's horse) outranking Domon as Master Asia's first (and favorite) student!
And then the series continues into the Gundam Wing adaptation, only with Wing characters added and creating new rivalries with the Gundam Fighters.
Ultimately crowning in the G-Unit/The Last Outpost manga, in which they included characters from the two above series, G-Unit, and Gundam X, and featured a block of strips that included characters from the original series, Gundam 0080, and Gundam 0083.